Question: The pond is completely full of water.
Sumeet wants to empty the pond so he can clean it.
Sumeet uses a pump to empty the pond.
The volume of water in the pond decreases at a constant rate.
The level of the water in the pond goes down by 20 cm in the first 30 minutes.
Work out how much more time Sumeet has to wait for the pump to empty the pond completely.
1. **State the problem:**
We have a pond shaped like a prism with dimensions length $= 2$ m, width $= 1$ m, and height $= 1.3$ m.
The water level drops by $20$ cm ($0.2$ m) in $30$ minutes at a constant rate.
We need to find how much more time it will take to empty the pond completely.
2. **Calculate the total height of water to be pumped out:**
The pond is full, so the total height of water is $1.3$ m.
3. **Calculate the rate of water level drop per minute:**
Water level drop in $30$ minutes = $0.2$ m
Rate $= \frac{0.2\text{ m}}{30\text{ min}} = \frac{1}{150}$ m/min
4. **Calculate the remaining height of water to be pumped out:**
Remaining height $= 1.3 - 0.2 = 1.1$ m
5. **Calculate the time to pump out the remaining water:**
Time $= \frac{\text{remaining height}}{\text{rate}} = \frac{1.1}{\frac{1}{150}} = 1.1 \times 150 = 165$ minutes
6. **Convert time to hours and minutes:**
$165$ minutes $= 2$ hours and $45$ minutes
**Final answer:**
Sumeet has to wait $165$ minutes or $2$ hours and $45$ minutes more to empty the pond completely.